That also happens in reality at a rate of about 0.1 degrees per 10 km. Because of changes in pressure and airflow during flight, the pilot\autopilot automatically makes that small adjustment to fly level. In KSP the scale is much smaller but atmospheric variations aren't modelled, so unless the plane is trimmed for level flight it will simply fly up to a stall. The SAS doesn't know you're in the atmosphere and does what it does in space; which is to LOCK your attitude to the star on the horizon your nose is pointing at. If you have enough thrust you'll eventually reach that star, but you'll leave Kerbin first, going up